Topological-recursion quantization conjecture for 2-functions

Let $\mathbf{T}$ be the set of 2-functions and let $W\in\mathbf{T}$. Construct a spectral curve $\mathcal{C}_W$ associated with $W$, apply topological recursion to obtain symplectic invariants $F_{g,n}(\mathcal{C}_W)$, and let $F(\mathcal{C}_W)$ be the generating function formed from the terms $F_{g,1}(\mathcal{C}_W)$. Topological-recursion quantization conjecture. The function $F(\mathcal{C}_W)$ is a quantum 2-function for every $W\in\mathbf{T}$. This proposes a converse to the classical-limit relationship between 2-functions and quantum 2-functions, but the source gives no resolution of the claim.